%I A033996
%S A033996 0,8,24,48,80,120,168,224,288,360,440,528,624,728,840,960,1088,1224,
%T A033996 1368,1520,1680,1848,2024,2208,2400,2600,2808,3024,3248,3480,3720,3968,
%U A033996 4224,4488,4760,5040,5328,5624,5928,6240,6560,6888,7224,7568,7920,8280
%N A033996 8 times triangular numbers.
%C A033996 Write 0,1,2,... in clockwise spiral; sequence gives numbers on one of 
               4 diagonals.
%C A033996 Also numbers of the form n^2-1 which are always divisible by 8. See link 
               for proof. - Cino Hilliard (hillcino368(AT)gmail.com), Mar 02 2003
%C A033996 Also, least m>n such that T(m)*T(n) is a square and more precisely that 
               of A055112(n). {T(n)=A000217(n)} - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               May 14 2004
%C A033996 Or, product of nth even number and nth even nonprime. - Juri-Stepan Gerasimov(2stepan(AT)rambler.ru), 
               Jul 26 2009
%C A033996 Except for the first term, a(n)=8*n+a(n-1), (with a(1)=8) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
%D A033996 Stuart M. Ellerstein, J. Recreational Math. 29 (3) 188, 1998.
%D A033996 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, 
               Reading, MA, 2nd ed., 1994, p. 99.
%H A033996 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A033996 Cino Hilliard, <a href="http://groups.msn.com/BC2LCC/8dividesn21firoddn.msnw">
               8 divides n^2-1 </a>.
%H A033996 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               KnightsTourGraph.html">Knight's Tour Graph</a>
%H A033996 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HamiltonianPath.html">Hamiltonian Path</a>
%F A033996 4n^2+4n. G.f.: A(x) = 8*x/(1-x)^3.
%F A033996 a(n)=A016754(n)-1=2*A046092(n)=4*A002378(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               May 25 2004
%F A033996 a(n)=A049598-A046092; a(n)=A124080-A002378. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 06 2007
%F A033996 a(n) = A000217(n)*8. [From Omar E. Pol (info(AT)polprimos.com), Dec 12 
               2008]
%F A033996 a(n)=A005843(n)*A163300(n). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Jul 26 2009]
%F A033996 a(n)=8*n+a(n-1)-8 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 12 2009]
%e A033996 16 17 18 19 ...
%e A033996 15 4 5 6 ...
%e A033996 14 3 0 7 ...
%e A033996 13 2 1 8 ...
%e A033996 For n=2, a(2)=8*2+0-8=8; n=3, a(3)=8*3+8-8=24; n=4, a(4)=8*4+24-8=48 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
%p A033996 [seq(8*binomial(n,2),n=1..46)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 24 2006
%p A033996 with(finance):seq(add(futurevalue( k, 3, 2),k=0..n)/2,n=0..45); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008
%p A033996 with(finance):seq(add(futurevalue(n,1,2),k=0..n),n=0..45); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008
%t A033996 s=0;lst={s};Do[s+=n++ +8;AppendTo[lst, s], {n, 0, 7!, 8}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
%o A033996 (PARI) nsqm1(n) = { forstep(x=1,n,2, y = x*x-1; print1(y" ") ) }
%Y A033996 Cf. A016754, A028896, A027468.
%Y A033996 Sequences from spirals: A001107, A002939, A007742, A033951, A033952, 
               A033953, A033954, A033989, A033990, A033991, A002943, A033996, A033988.
%Y A033996 Cf. A028895, A046092, A045943, A002378, A028896, A024966.
%Y A033996 Cf. A049598, A046092, A124080, A002378.
%Y A033996 Cf. A000217. [From Omar E. Pol (info(AT)polprimos.com), Dec 12 2008]
%Y A033996 Sequence in context: A063403 A122812 A022763 this_sequence A146980 A028612 
               A068857
%Y A033996 Adjacent sequences: A033993 A033994 A033995 this_sequence A033997 A033998 
               A033999
%K A033996 nonn,easy
%O A033996 0,2
%A A033996 N. J. A. Sloane (njas(AT)research.att.com).
%E A033996 More terms from Cino Hilliard (hillcino368(AT)gmail.com), Mar 02 2003